Computing Neurons - An Introduction - Kenji Doya doya@oist.jp

1. Computing Neurons- An Introduction -Kenji Doyadoya@oist.jp Neural Computation Unit Initial Research ProjectOkinawa Institute of Science and Technology

2. `Computing Neurons’ • What/How are neurons computing? • Network • Single cell • Synapse • How can we compute neurons? • Dendrites, channels, receptors, cascades • Simulators, databases • Understanding by re-creating

3. Multiple Scales • (Churchland & Sejnowski 1992)

4. Outline • Neurobiology • Nervous system • Neurons • Synapses • Computation • Functions • Dynamical systems • Learning

5. Nervous System • Forebrain • Cerebral cortex (a) • neocortex • paleocortex: olfactory cortex • archicortex: basal forebrain, hippocampus • Basal nuclei (b) • neostriatum: caudate, putamen • paleostriatum: globus pallidus • archistriatum: amygdala • Diencephalon • thalamus (c) • hypothalamus (d) • Brain stem & Cerebellum • Midbrain (e) • Hindbrain • pons (f) • cerebellum (g) • Medulla (h) • Spinal cord (i)

6. Neurons • Cortex Basal Ganglia Cerebellum • (Takeshi Kaneko) (Erik De Schutter)

7. Hodgkin-Huxley Model • Neuron as electric circuit

8. a Close 1-x Open x b Ionic Channels • Open-close dynamics • Identification by ‘voltage-clamp’ experiments

9. ‘Current-Clamp’ Experiments

10. i-1 i i+1 Axons and Dendrites • Compartment model • ga(Vi+1-Vi)+ga(Vi-1-Vi) = C dVi/dt + Im(Vi,mi,hi,ni)

11. Synapses • spike  transmitter  receptor  conductance

12. Transmitters Acetylcholine Glutamate GABA Dopamine/Serotonin Noradrenaline/Histamine Enkephaline Substance-P Adenosine/ATP NO Ionotropic Receptors Excitatory: Na+, Ca2+ Inhibitory: K+, Cl- Metabotropic Receptors G-protein cyclic AMP ... Transmitters and Receptors

13. Purkinje cell (Doi et al. 2005) Medium-spiny neuron (Nakano et al. 2006) Signal ‘Transduction’ Pathway

14. Molecular Reactions • Binding reaction • Enzymatic reaction: Michaelis-Menten equation

15. Protein Synthesis, Gene Regulation • DNA  mRNA  protein • promoter/inhibitor

16. Outline • Neurobiology • Nervous system • Neurons • Synapses • Computation • Functions • Dynamical systems • Learning

17. Functions • mapping: x  y ...can be many-to-many • function: y = f(x) ...unique output • Linear • f(x1+x2) = f(x1) + f(x2) • f(ax) = a f(x) • y = Ax • scale, rotation, shear • Affine: y = Ax+b • translation • Nonlinear

18. Dynamical Systems • Discrete: x(t+1) = f( x(t)) • Continuous: dx(t)/dt = f( x(t)) • Linear: dx(t)/dt = Ax(t) • exponential • sinusoidal • Nonlinear • multiple equilibria • limit cycle • Bifurcation

19. Unsupervised Learning output input Reinforcement Learning reward output input Supervised Learning target + error - output input Learning • Supervised • samples (x1,y1), (x2,y2),... • function y = f(x) • Reinforcement • state x, action y, reward r • policy y = f(x) or P(y|x) • Unsupervised • samples x1, x2,... • probabilistic model P(x|y)

20. Survival catch battery packs Reproduction copy ‘genes’ through IR ports Rewards for Cyber Rodents

21. Cerebral Cortex：Unsupervised Learning output input Basal Ganglia: Reinforcement Learning reward output input Cerebellum: Supervised Learning target + error - output input Specialization by Learning Algorithms (Doya, 1999) Cortex Basal thalamus Ganglia SN Cerebellum IO

22. Dynamical systems Bard Ermentrout Shin Ishii Network Geoff Goodhill Jeff Wickens Sydney Brenner Felix Schuermann Neuron Erik DeSchutter Haruhiko Bito Synapse Susumu Tonegawa Terry Sejnowski Upi Bhalla Nicolas Le Novere Shinya Kuroda Ion Moraru David Holcman Yang Dan OCNC 2006 Topics

23. Questions • How do they work? • What are the complexities for? • Are they robust? • How to justify/falsify?